Rough set systems induced by equivalences have been proved to exhibit polymorphic logical behaviours in dependence on the extension of the set of completely defined objects. They give a rise to semi-simple Nelson algebras, hence three-valued Lukasiewicz algebras and regular double Stone algebras. Additionally, it has been shown that in the presence of completely defined objects, they fulfil a f...

We investigate a natural Heyting algebra structure on the set of Dyck paths of the same length. We provide a geometrical description of the operations of pseudocomplement and relative pseudocomplement, as well as of regular elements. We also find a logic-theoretic interpretation of such Heyting algebras, which we call Dyck algebras, by showing that they are the algebraic counterpart of a certai...

In this paper we study the lattice of restricted subalgebras a Lie algebra. particular, consider those algebras in which is dually atomistic, lower or upper semimodular, every subalgebra quasi-ideal. The fact that there are one-dimensional not results some these conditions being weaker than for corresponding non-restricted case.

In this paper, we explore general relationships among negations, convex Archimedean nilpotent t-norms, and automorphisms of the unit interval I. Each nilpotent t-norm has a (strong) negation naturally associated with it, namely, 4 (x) = W fy 2 [0; 1] : x4 y = 0g. The same negation is determined by the formula 4 (x) = f 1 (f (0) =f (x)) where f is a (multiplicative) generating function for the t...

We examine the notion of bisimulation and its ramifications, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relati...

Generalizing relational structures and formal languages to structures whose relations are evaluated by elements of a lattice, we show that such structure classes form a Heyting algebra if and only if the evaluation lattice is a Heyting algebra. Hence various new and some older results obtained for Heyting algebras can be applied to such structure classes.

We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula. Résumé. Nous introduisons une nouvelle base des fonctions symé...

A piggyback duality and a translation process between this one and a Priestley duality for each subvariety of involutive Stone algebras and regular o-De Morgan algebras is presented. As a consequence we describe free algebras and the prime spectrum of each subvariety.

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

Abstract. A new form of α-compactness is introduced in L-topological spaces by α-open L-sets and their inequality where L is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice L. It can also be characterized by means of α-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented and the re...